Average, Mixture and Alligation Question 5 - CAT 2021
In a football tournament, a player has played a certain number of matches and 10 more matches are to be played. If he scores a total of one goal over the next 10 matches, his overall average will be 0.15 goals per match. On the other hand, if he scores a total of two goals over the next 10 matches, his overall average will be 0.2 goals per match. The number of matches he has played is:
Step-by-Step Explanation
Let M be the number of matches the player has already played, and G be the total number of goals he scored in those matches. Ten more matches will be played, making the new total number of matches M + 10.
- Scenario 1 (1 goal scored in the next 10 matches):
(G + 1) / (M + 10) = 0.15 ⟹ G + 1 = 0.15(M + 10) --- (Equation 1)
- Scenario 2 (2 goals scored in the next 10 matches):
(G + 2) / (M + 10) = 0.20 ⟹ G + 2 = 0.20(M + 10) --- (Equation 2)
- Subtract Equation 1 from Equation 2:
G + 2 − G − 1 = 0.20(M + 10) − 0.15(M + 10)
1 = 0.05(M + 10)
M + 10 = 1 / 0.05 = 20 ⟹ M = 10 matches
The number of matches he has played so far is 10.
Correct Answer: 10
💡 FundaMakers Tip:
Look directly at the net difference between the two hypothetical conditions. Adding exactly 1 more goal (2 − 1) increases the final overall career average by 0.20 − 0.15 = 0.05 goals per match.
Since Total Matches × 0.05 = 1, the total number of matches must be 20. Subtracting the 10 remaining matches gives the answer immediately.